Question

Monthly payments on a $165,000 mortgage are based on an interest rate of 6.6% compounded semiannually and a 30-year amortization. If a $5000 prepayment is made along with the thirty-second payment: (Do not round the intermediate calculations.)

a. How much will the amortization period be shortened? (Round UP to the next whole number.)

  

The amortization period will be shortened by years and month(s).

  

b.What will be the principal balance after four years? (Round your answer to two decimal places.)

  

Balance after 4 years will be $.

Answer 1

Sol:

a) The amortization period will be shortened by 2 years and 2 months.

b) Loan Balance after 4 years will be $ 156,863.94

Explanation:

Using Financial Calculator

Step 1 : Calculation of Monthly payment

Input

• P/Y = 12
• C/Y = 2
• I/Y = 6.6
• N = 30*12 = 360
• PV = -165000
• FV = 0

and

Press CPT and then PMT

You will get Monthly Payment = 1044.1103

Step 2 : Calculation of Loan outstanding after 32nd Payment after considering additional payment

Input

• P/Y = 12
• C/Y = 2
• I/Y = 6.6
• N = 32
• PMT= 1044.1103
• PV = -165000

and

Press CPT and then FV

You will get Loan outstanding after 32nd Payment before considering additional payment = 159813.85

Loan outstanding after 32nd Payment after considering additional payment = Loan outstanding after 32nd Payment before considering additional payment -Additional payment

Loan outstanding after 32nd Payment after considering additional payment = 159813.85-5000

Loan outstanding after 32nd Payment after considering additional payment = 154813.85

Step 3 : Calculation of Remaining No of Period after additional payment

Input

• P/Y = 12
• C/Y = 2
• I/Y = 6.6
• PMT= 1044.1103
• PV = -154813.85
• FV = 0

and

Press CPT and then N

You will get Remaining No of Period after additional payment = 301.64 Months or 302 Month (rounded up)

Step 4 : Calculation of Amortization period be shortened

Amortization period be shortened = Actual No of payment initially - Total No of payment when additional payment is made

Amortization period be shortened = 360 - (32+302)

Amortization period be shortened = 26 Months

Amortization period be shortened = 2 Years and 2 Months

Step 5 : Calculation of principal balance after four years

Input

• P/Y = 12
• C/Y = 2
• I/Y = 6.6
• N = (4*12 - 32) = 16
• PMT= 1044.1103
• PV = -154813.85

and

Press CPT and then FV

You will get Loan Balance after 4 years will be = 156,863.94